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RESEARCH PAPERS

Chaos in a Weakly Nonlinear Oscillator With Parametric and External Resonances

[+] Author and Article Information
K. Yagasaki

Department of Mechanical Engineering, Tamagawa University, Machida, Tokyo 194, Japan

J. Appl. Mech 58(1), 244-250 (Mar 01, 1991) (7 pages) doi:10.1115/1.2897158 History: Received April 17, 1989; Revised March 01, 1990; Online March 31, 2008

Abstract

This paper describes a study of the chaotic dynamics of a weakly nonlinear single degree-of-freedom system subjected to combined parametric and external excitation. We consider a case of double resonance in which primary resonances, with respect to parametric and external forces, exist simultaneously. By using the averaging method and Melnikov’s technique, it is shown that chaos may occur in certain parameter regions. These chaotic motions result from the existence of orbits homoclinic to a normally hyperbolic invariant torus which corresponds to a hyperbolic periodic orbit in the averaged system. The mechanism and structure of chaos in this situation are also described. Furthermore, the existence of steady-state chaos is demonstrated by numerical simulation.

Copyright © 1991 by The American Society of Mechanical Engineers
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